Pullulan and Dextran: Uncommon Composition Dependent Flory

Biomacromolecules 2008, 9, 1691–1697

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Pullulan and Dextran: Uncommon Composition Dependent Flory–Huggins Interaction Parameters of their Aqueous Solutions John Eckelt,† Rei Sugaya, and Bernhard A. Wolf* Institut fu¸r Physikalische Chemie der Johannes Gutenberg-Universita¸t Mainz and Materialwissenschaftliches Forschungszentrum der Universita¸t Mainz, Welder-Weg 13, D-55099 Mainz, Germany, and WEE-Solve GmbH, Auf der Burg 6, D-55130 Mainz, Germany Received February 27, 2008; Revised Manuscript Received March 11, 2008

Vapor pressure measurements were performed for aqueous solutions of pullulan (Mw 280 kg/mol) and dextran (Mw 60 and 2100 kg/mol, respectively) at 25, 37.5, and 50 °C. The Flory–Huggins interaction parameters obtained from these measurements, plus information on dilute solutions taken from the literature, show that water is a better solvent for pullulan than for dextran. Furthermore, they evince uncommon composition dependencies, including the concurrent appearance of two extrema, a minimum at moderate polymer concentration and a maximum at high polymer concentration. To model these findings, a previously established approach, subdividing the mixing process into two clearly separable steps, was generalized to account for specific interactions between water and polysaccharide segments. Three adjustable parameters suffice to describe the results quantitatively; according to their numerical values, the reasons for the solubility of polysaccharides in water, as compared with that of synthetic polymers in organic solvents, differ in a principal manner. In the former case, the main driving force comes from the first step (contact formation between the components), whereas it is the second step (conformational relaxation) that is advantageous in the latter case.

1. Introduction The motivation for the present work comes from two sources: one lies in the central importance of aqueous solutions of polysaccharides in many areas and in the fact that the thermodynamic understanding of these systems is far from being satisfactory; and the other incentive originates from a recent approach explaining several otherwise unconceivable phenomena observed with solutions of synthetic polymers in organic solvents by subdividing the mixing process into two clearly separable steps. We wanted to investigate to which extent this alternative thermodynamic modeling can also contribute to a better understanding of aqueous solutions of polysaccharides. Numerous review articles1–4 have appeared in the past years, describing in great detail the outstanding role of pullulan and dextran in the fields of biology, medicine, cosmetics, and technology, particularly in the food industry. The three most recent publications using the new approach5 deal with system water/cellulose6 (exhibiting a large miscibility gap between the components), with the question of how the system specific parameters of this concept are composed of enthalpy and entropy contributions7 and apply the concept to random copolymers.8 The extensive experimental data obtained by means of the present vapor pressure and light scattering experiments at different temperatures manifests that aqueous solutions of polysaccharides exhibit additional features, which cannot be described by means of only two adjustable parameters in contrast to the normal situation encountered with solutions of synthetic polymers in organic solvents. By adequately considering additional possibilities for the interaction between individual water molecules and the glucose units of the polymer it is, however, * To whom correspondence should be addressed. E-mail: bernhard.wolf@ uni-mainz.de. † WEE-Solve GmbH.

possible to model the newly observed phenomena, as will be demonstrated in the theoretical section after a brief recapitulation of the status quo ante.

2. Theory An extended Flory–Huggins theory has proven to be of great help for the thermodynamic description of solutions of synthetic polymers in organic solvents.5 The starting point of this approach is the segment molar Gibbs energy of mixing, which is usually formulated for binary systems as )

∆G ( φ ) 1 - φ) ln(1 - φ) + ln(φ) + gφ (1 - φ) RT N

(1)

where φ is the volume fraction of the polymer and N is the number of segments (defined as the ratio of the molar volume of the polymer divided by that of the solvent). The first two terms on the right-hand side of this relation formulate the combinatorial mixing behavior, whereas the third term represents the noncombinatorial contribution to the total effect. The thermodynamic particularities of a given system are (with the exception of N) exclusively contained in the integral interaction parameter g. Initially, it was thought that g depends only on temperature and pressure, but not on the composition of the mixture. However, experimental evidence has soon demonstrated that g may be, and usually indeed is, a complicated function of φ. For a mathematical description of these characteristic features of g(φ), we have proposed the following expression5

g)

R (1 - ν)(1 - νφ)

- ζ(1 + (1 - λ)φ)

(2)

It is based on a conceptual subdivision of mixing into two steps and consequently consists of two terms: The first quantifies

10.1021/bm800217y CCC: $40.75  2008 American Chemical Society Published on Web 05/10/2008

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Eckelt et al.

the effect of contacting a polymer segment with a solvent molecule, keeping the conformation of the environment as it was before mixing; R/(1 - υ) represents the contribution of this step in the limit of infinite dilution; the parameter υ accounts for the fact that the molecular surfaces (decisive at least for the enthalpic interaction) of the two types of segments (equal in their volume) are normally not identical. The second term is required because of the ability of most macromolecules to change their conformation after the first mixing step to minimize the Gibbs energy of the system. This conformational relaxation is quantified by the parameters ζ and λ, where the former becomes zero under theta conditions and the latter is easily accessible from independent experimental information. For most systems, it can without noteworthy loss of accuracy be set equal to 0.5. For practical purposes, eq 2 is not of much use, because only the chemical potentials, that is, the derivatives of g, are normally experimentally accessible. For this reason, the original Flory– Huggins interaction parameter χ was introduced in terms of the chemical potential of the solvent (which is typically determined via scattering experiments, osmosis or vapor pressures) by means of the following expression )

∆Gsolvent 1 ) ln(1 - φ) + 1 - φ + χφ2 RT N

(

)

(3)

where the differential interaction parameter is related to the integral interaction parameter by

χ ) g - (1 - φ)

∂g ∂φ

(4)

If the vapor above the polymer solutions behaves like an ideal gas one can write )

()

∆Gsolvent p ) ln RT po

(5)

This means that it is possible to calculate χ directly from the measured vapor pressure p subject to the condition of p being sufficiently different from po (vapor pressure of the solvent), as is the case for concentrated polymer solutions. Light scattering or osmosis gives access to this information for dilute solutions. The limiting value χο, describing the system in the range of pair interaction between the solute is related to the second osmotic virial coefficient A2 by

1 χo ) - A2F22Vj1 2

(6)

j 1 is the molar volume of F2 is the density of the polymer and V the solvent. By means of eq 4, we obtain the following expression for χ from eq 2

χ)

R (1 - νφ)2

- ζ(λ + 2(1 - λ)φ)

(7)

Because of the already mentioned fact that the parameter λ is in the great majority of cases very close to 0.5, it is possible to reduce the number of adjustable parameters from four to three by condensing ζ and λ into one parameter and setting the remaining λ term equal to 0.5. In this manner, the above expression becomes

χ≈

R (1 - νφ)2

- ζλ(1 + 2φ)

(8)

The number of adjustable parameter can still be reduced by one, if a measured χο value is available, because eq 7 yields the following expression for χο as φ f 0

χo ) R - ζλ

(9)

so that eq 8 becomes

χ≈

χo + ζλ - ζλ(1 + 2φ) (1 - νφ)2

(10)

Considering χο as a system specific parameter, which does not need adjustment, we end up with only two parameters to describe the isothermal thermodynamic behavior of a normal polymer solution quantitatively, namely, ζλ and υ. This special treatment of the data point at infinite dilution is justified by the special character of eq 6: Due to the fact that the second osmotic virial coefficient represents the small difference between two almost equal quantities (0.5 and χο), it can be measured with such high an accuracy, that the error in χο (calculated from A2) is negligible in comparison with that of the rest of χ values at finite polymer concentration. The present measurement for aqueous solutions of polysaccharides manifest that eq 7, which works very well with all solutions of synthetic polymers in organic solvents studied so far, fails. It is obvious that particular interactions between the solvent and the solute require modifications in the relation for the integral interaction parameter g. The suggesting idea that ζλ, υ, or both parameters are no longer independent of polymer concentration proved to be unrealistic. For this reason, we have added a term to eq 2, which accounts for extra contributions to the residual Gibbs energy of mixing. The quadratic composition dependence of this contribution was chosen on the basis of the assumption that special interactions exist between pairs of the polysaccharide molecules. Extra contributions of intermolecular hydrogen bonds, which increase with the probability of pair formation, could be a speculative explanation for the necessity of this term.

g)

R (1 - ν)(1 - νφ)

- ζ(1 + (1 - λ)φ) + φ2

(11)

From this relation, we obtain by means of eq 4

χ≈

χo + ζλ - ζλ(1 + 2φ) + φ(3φ - 2) (1 - νφ)2

(12)

if we perform the same substitutions and simplifications as before. The present experimental data are evaluated by means of the above relation, adjusting three parameters, namely, ζλ, υ, and ω j , where the third parameter accounts for the extra effects observed with aqueous solutions of the polysaccharides. For the assessment of the practical suitability of theoretical expressions, it is important to check whether they reproduce the actually observed phase state. The mere ability to describe measured chemical potentials within experimental error is no guarantee; the reason lies in the necessity to integrate the equations of the form of eqs 10 or 12 to obtain the integral interaction parameter g. This parameter is required for the calculation of the Gibbs energy of mixing (eq 1) to obtain the second derivative, which decides on the phase state of the system. For completely miscible components, the second derivative is for all compositions positive, whereas it becomes negative in case of miscibility gaps, where this function becomes zero when the spinodal conditions are reached. The following relation was used to calculate g from the measured χ values

g)-

1

∫ 1-φ χdφ (

(1 - φ ) 1

)

(13)

This integration plus the two subsequent steps of differentiation make the assessment of the phase state based on χ(φ) very

Pullulan and Dextran


Table 1. Polymer Samples and some Characteristic Parameters samples Pul 280w Dex 60w Dex 2100w

U) A225 °C (10-4 Mn (kg Mw (kg F25 °C -1 -1 -1 -1 mol ) mol ) Mw/Mn (g mL ) mol cm3 g-2) 79.7 27.8 300.0

277.0 59.5 2100.0

2.5 1.1 6.0

1.609 1.3811 2.0111

2.210 4.5612 0.7413

sensitive with respect to the mathematical details of the modeling. The expression for the second derivative resulting from the present approach (eq 12) reads

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Table 2. System Specific Parameters of Eq 12 for the System H2O/Pul 280w at Different Temperaturesa Pul 280w, 25 °C

Pul 280w, 37.5 °C

Pul 280w, 50 °C

χ0 0.491 χ0 0.488 χ0 0.491 υ 0.815 (0.032 υ 0.753 (0.014 υ 0.593 (0.04 ζλ -0.761 (0.057 ζλ -0.858 (0.05 ζλ -1.97 (0.891 ω j 2.384 (0.393 ω j 2.183 (0.286 ω j 2.985 (0.919 R -0.27 R -0.370 R -1.479 a

The 25 °C are calculated anew from p

vap

.

)

1 ∂2∆G 1 1 2R ) + + (1 - φ ) RT ∂φ2 Nφ (1 - νφ)3 2(R - χo)(1 + 3φ) + 6φ (1 - 2φ) (14) 3. Materials Pullulan (Pul 280w) and one dextran sample (Dex 60w) were kindly donated by Polymer Standard Service, Mainz, Germany (PSS), and a further dextran sample (Dex 2100w) was purchased from Amersham Pharmacia Biotech AB (Uppsala, Sweden). Table 1 gives the molecular weights of the samples as determined by means of GPC. In the case of Dex 2100w, the information stems from the supplier. The GPC measurements were carried out at room temperature in aqueous solution (containing 8.5 g of NaNO3 and 4.2 g of NaHCO3 per liter) using the columns HEMA BIO 40, HEMA BIO 1000, and SUPREMA 300 supplied by PSS. The column was calibrated against dextran samples (supplied by PSS). The molar mass for the pullulan sample was obtained by means of universal calibration using the following Kuhn-Mark–Houwink parameters10 for pure water: Kdextrane ) 0.0978 mL/g, adextran ) 0.5, Kpullulan ) 0.0221 mL/g, apullulan ) 0.66. Because of the fact that the eluent contains salt, the obtained molar mass is apparent only. Bidistilled water was used as solvent for all polymers. Its temperature dependent densities 0.997 g mL-1 (25 °C), 0.993 (37.5 °C), and 0.988 (50 °C) were taken from the literature.14

4. Procedures The reduced vapor pressures of the aqueous polysaccharide solutions were determined by means of a gas chromatograph (Shimadzu GC14B, Kyoto, Japan) in combination with a head space sampler (Dani HSS 3950, Milano, Italy). The method (HSGC) is described in detail elsewhere.15 To achieve phase equilibria within a reasonable time, the polymer was cast in thin films (0.005-0.02 mm) on glass beads of about 4 mm diameter. For this purpose, the polysaccharides were dissolved in water (concentrations up to 20 wt %) and poured over the glass beads. After exhaustive drying at room temperature under oil pump vacuum, the dry films were loaded with water via the gas phase to yield polymer concentrations in the range from 80 to 97 wt %. To prepare lower concentrations in the range from 30 to 80 wt %, liquid water was added. The pullulan solutions were thermostatted for two days prior to the measurement; both dextran samples were measured after one day; and Dex 60w was additionally kept at constant temperature for one week and for three weeks after sample preparation to investigate possible influences of crystallization on the measured vapor pressures. To obtain reliable data, the vapor pressure was measured six times for each sample.

5. Results With both polysaccharide solutions, the vapor pressure measurements were performed at 25.0, 37.5, and 50.0 °C; the

Figure 1. Reduced vapor pressure of water, measured for aqueous solutions of Pul 280w at 37.5 °C. The full curve is modeled by means of the eqs 3, 5, and 12 and the parameters of Table 2. The broken line is the best fit obtained by means of eq 10.

Figure 2. Composition dependence of the Flory-Huggins interaction parameter χ for the system H2O/Pul 280w at 37.5 °C. The full curve is modeled by means of the eqs 3, 5, and 12 and the parameters of Table 2. The broken line is the best fit obtained by means of eq 10.

Flory–Huggins interaction parameter χο in the limit of high dilution were calculated from published A2 values.10,12,13 The number of segments, N, necessary to calculate χ from the vapor pressures according to eqs 3 and 5 were obtained by means of the temperature-dependent molar volumes of water14 in combination with the polymer densities for 25 °C (cf. Table 1). This simplification remains inconsequential as compared with all other errors. 5.1. Pullulan. Figure 1 gives an example for the primary data obtained with this polymer; the arrow bars are pessimistic estimates. The full curve was calculated by means of eqs 3, 5, and 12, using the system specific parameters collected in Table 2. The broken line shows the modeling on the basis of eq 10 instead of eq 12, that is, under the neglect of specific interactions between the components, quantified by the extra term ω j φ2 in the expression for the integral Flory–Huggins interaction parameter g. How the differential interaction parameter depends on φ is shown in Figure 2; these values were calculated from the reduced vapor pressures shown in Figure 1 by means of eqs 3 and 5, except for χο, which stems from second osmotic virial coefficient A2 and was obtained via eq 6. The full curve displays

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Figure 3. Flory–Huggins interaction parameters measured (K, 50 °C; O, 37.5 °C; and k, 25 °C) for the system H2O/Pul 280w and their modeling by means of eq 12.

Eckelt et al.

Figure 5. Flory–Huggins interaction parameters measured (K: 50 °C; O: 37.5 °C, and k: 25 °C) for the system H2O/Dex 60w and their modeling by means of eq 12. Table 3. System-Specific Parameters of Eq 12 for the System H2O/Dex 60w at Different Temperatures Dex 60w, 25 °C

Dex 60w, 37.5 °C

Dex 60w, 50 °C

χ0 0.476 χ0 0.478 χ0 0.481 υ 0.951 (0.037 υ 0.8 (0.179 υ 0.797 (0.059 ζλ -0.532 (0.026 ζλ -0.657 (0.224 ζλ -0.726 (0.101 ω j 0.821 (0.745 ω j 0.514 (0.986 ω j 1.833 (1.366 R -0.056 R -0.179 R -0.245

Figure 4. Reduced vapor pressures of aqueous solutions of Dex 60w measured at 25 °C and the equilibration times of 1 day, 1 week, and 3 weeks, respectively. The curve is a guide to the eye only.

the modeling by means of eq 12 (for the parameters, cf. Table 2), whereas the broken line represents the best fit obtained with eq 10. How a change in temperature influences the interaction parameters and χ(φ) is depicted in Figure 3. 5.2. Dextran. For the present measurements with this polysaccharide, we have chosen one low molecular weight sample and one high molecular weight sample. The most obvious difference between them concerns the time dependence of the transparency of their solutions. The solutions of Dex 2100w remain totally transparent at all temperatures and concentration, whereas that of Dex 60w become within the composition range 0.4–0.6 cloudy upon a prolonged standing. A comparison of the vapor pressure measured for clear and for turbid mixtures did, however, show (cf. Figure 4) that the effects resulting from that phenomenon remain minor. On the basis of the observations shown in Figure 4, we have all further measurements with Dex 60w and with Dex 2100w performed after 1 day of equilibration. The composition dependence of χ resulting from these measurements and from the χο values taken from literature12,13 for Dex 60w are presented in Figure 5. The corresponding system specific parameters are collected in Table 3. Figure 6 displays the corresponding results for Dex 2100w, the higher molecular weight sample of dextran; the system specific parameters are given in Table 4.

6. Discussion Before starting with the assessment of the different findings, it appears appropriate to spend a few words on the importance of the phenomena that might influence the interpretation of the primary experimental data. First of all, the glassy solidification of the polysaccharide solutions at large φ values requires a comment. According to earlier studies of these effects,16 it

depends on the particular polymer/solvent system whether this transition can be seen in the vapor pressure data. With polystyrene solutions in toluene, the vapor pressures as a function of composition exhibit discontinuities, indicating the coexistence of two different kinds of microphases. In contrast to that, the vapor pressure curve for polystyrene solutions in cyclohexane does in no way display the freezing in of the mixtures; it extrapolates smoothly up to the pure polymer. From the present data it is obvious that the aqueous solutions of the polysaccharides under investigation behave like the latter system. The fact that the elimination of the data points which are likely located beyond the solidification concentration of the system does not change the results constitutes an additional corroboration of this assessment. A second source of uncertainty could come from the turbidity that develops upon standing with the solutions of the lower molecular weight dextran. As already pointed out earlier, this phenomenon also remains inconsequential within the experimental accuracy of the vapor pressure measurements. The most obvious observation of the present study consists of the fact that water is a much better solvent for pullulan than for dextran. This feature can be directly seen from the comparison of the vapor pressure data shown in Figure 7. Particularly at moderate polymer concentrations, the interaction of pullulan with water is so favorable that pvap falls markedly below that of the pure solvent in contrast to the system water/ dextran. To our knowledge there is also no other example for such a marked reduction at so low polymer concentrations. The differences between the two samples of dextran remain within experimental error; nevertheless, there might well exist some effect of molar mass, because the branching probability increases with rising M of this polysaccharide.17 The vapor pressure data displayed in Figure 7 translate into Flory–Huggins interaction parameters, as demonstrated in Figure 8. During the last years a more detailed analysis of experimentally determined dependencies χ(φ) has demonstrated beyond doubt that nonlinear dependencies are the rule rather than the exception. According to experience, minima in this function are not uncommon;5 recently, a maximum in χ(φ) has also been reported.8 However, the results with the present aqueous solutions of polysaccharides are the first examples for the



Figure 6. Flory–Huggins interaction parameters measured (K, 50 °C; O, 37.5 °C; and k, 25 °C) for the system H2O/Dex 2100w and their modeling by means of eq 12. Table 4. System Specific Parameters of Eq 12 for the System Dex 2100w Dex 2100w, 25 °C

Dex 2100w, 37.5 °C

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Figure 7. Comparison of the vapor pressures above aqueous solutions of the two types of polysaccharides at 37.5 °C, calculated by means of the eqs 3, 5, and 12 and the parameters of Tables 2–4; the broken line stands for Dex 60w.

Dex 2100w, 50 °C

0.495 χ0 0.497 χ0 0.495 χ0 υ 0.878 (0.011 υ 0.814 (0.039 υ 0.775 (0.019 ζλ -0.614 (0.021 ζλ -0.662 (0.058 ζλ -0.733 (0.027 ω j 1.643 (0.363 ω j 0.636 (0.309 ω j 1.285 (0.001 R -0.119 R R -0.237

occurrence of two extrema. It should be emphasized in this context that this feature does not depend on the particular way of modeling, but can already be seen in the raw data (Figure 2 gives an example). It would of course be very interesting to know more about the molecular reasons for such a complicated behavior. A first attempt for a better understanding will be presented in the context of a discussion of the physical meaning of the system specific interaction parameter. But before that it appears expedient to demonstrate that the modeling of the data along the usual lines fails. The breakdown of the hitherto quite successful eqs 2 and 3 has already been visualized in Figures 1 and 2. Even if one would assume unreasonably large experimental errors in χ and claim that the dotted line shown in Figure 2 describes reality fairly well, this option must be ruled out. The reason is that it yields a composition dependence of the second derivative of the total Gibbs energy, which results in an unstable area extending from φ almost zero up to φ ) 0.45. This modeling would consequently be in strong contradiction to the direct observation according to which the system remains homogeneous in the entire composition range at all temperatures studied. Modeling on the basis of other expressions, ignoring the occurrence of a minimum in χ(φ) at moderate polymer concentrations, produces similarly extended miscibility gaps. On the other hand, such two-phase areas are absent with the present modeling (eq 12). Like the shapes of χ(φ), the influences of temperature are qualitatively very similar for the solutions of the two types of polysaccharides. In the limit of low polymer concentrations, the heats of dilution (as measured by χο(T)) are very close to athermal, whereas they become pronouncedly exothermal for large φ values. In this concentration range the χ increases dramatically as T rises from 25 to 50 °C (cf. Figures 3, 5 and 6). The following paragraphs deal with the contributions of the individual system specific parameters of eq 12 to the composition and temperature dependence of the Flory–Huggins interaction parameter. Figure 9 shows the typical magnitude of these parameters, taking the results for the higher molecular weight dextran as an example, and demonstrates how a variation of temperature affects their values. The present approach requires,

Figure 8. Composition dependence of the Flory–Huggins interaction parameter χ for aqueous solutions of pullulan and dextran calculated by means of eq 12 and the parameters of Tables 2–4; the broken line stands for Dex 60w.

Figure 9. Temperature dependence of the system specific parameters, π, for the system H2O/Dex 2100w.

as already mentioned, three adjustable parameters, namely υ (specifying the first term of eq 12), ζλ (measuring the contribution of the conformational relaxation, i.e. the second term), and ω quantifying the third term. As already outlined earlier, an adjustment of R is not required because of the high precision of χο, which enables its elimination via eq 9. Nevertheless, this parameter is incorporated in Figure 9 for the reason that it represents the starting point of the present approach by measuring the effect associated with the separation of two contacting polymer segments belonging to different polymer chains by inserting a solvent molecule. When discussing the individual contributions of the three terms of eq 12 to the total effects one needs to keep in mind that (with the exception of υ) each parameter is made up of an enthalpy and of an entropy part; simple interpretations in terms of heats of mixing are thus impossible at this stage. A corresponding analysis can, however, be performed7 if sufficient experimental material on π(T) is available. According to the data shown in Figure 9, the enthalpy part of R is negative and that of ζλ (because of the negative

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sign of this term in eq 12) is positive. The situation with ω is presently unclear. For both systems and at all temperatures the first term acts strongly toward homogenizing the components: The favorable effect of the negative R increases considerably with rising polymer concentration because of the uncommonly high υ values, which can be rationalized18 in terms of the large surface to volume ratio of water as compared with that of the polymer segments. For the parameters shown in Figure 9, the contribution of the first term to the integral interaction parameter g changes from –1.8 at φ ) 0 to –6.0 at φ ) 1. In agreement with all previous observations, the second term of g or χ is unfavorable if the first term is advantageous and vice versa. The state reached when mixing the components under the condition that the rest of their molecular environment is kept as it was before that process cannot be upheld because it does not represent the minimum of the Gibbs energy of the system. Equilibrium is only reached upon a conformational relaxation during which the components rearrange adequately. The third term of the interaction parameters required for the description of the present systems is particularly and most likely a consequence of the many hydrogen bonds broken and established during the mixing process. Postulating the existence of isolated water molecules bridging two polymer segments via strong hydrogen bonds could for instance explain why the vapor pressure does not approach zero as φ f 1 in the usual linear manner. With the solutions of polysaccharides, the extrapolation of the linear part of the vapor pressure curve representing the data at high polymer concentration intersects the abscissa already at φ ≈ 0.95. According to the present measurements, this contribution to g is unfavorable for mixing. One possible explanation for this finding could lie in a predominance of the entropy part of this term, which should be highly negative because of the very special arrangement of the components required for such a “cross-linking” of polymer segments by inserting an isolated water molecule. Such arguing does not appear too far fetched in view of calorimetric evidence on the existence of two types of water in cellulose acetate membranes19 and on the thermal behavior of water in crosslinked dextran.20 Out of the three adjusted parameters υ, ζλ, and ω j , the precision of ω j is least, as documented in the different tables. There is, however, a good reason for that deficiency, namely, the lack of sufficient data in the range of moderate polymer concentrations. Even though the existence of the minima in χ(φ) is beyond doubt, its quantification in terms of ω j is difficult. The precision could, however, be raised considerably, for instance, by light scattering measurements up to higher polymer concentrations. Despite the necessity to introduce an extra term for the description of the aqueous polysaccharide solutions, a general interrelation between the parameters R and ζλ, observed with all systems studied so far, should remain valid because it concerns the infinitely dilute state for which the extra phenomena are of no importance. Figure 10 demonstrates that these data indeed fall on a common line. In view of eq 9 and the fact that the values of χο are almost always not too far from 0.5, the finding as such is not surprising. The truly valuable information consists in the location of the data for a given system along this line, that is, in the actual combination of R and ζλ, resulting in χο ≈ 0.5. Solutions of typical synthetic polymers lie without exception in the upper right quadrant; for them a thermodynamically favorable ζλ > 0 comes along with unfavorable R > 0; normal theta systems are according the present approach characterized by ζλ ) 0 and R ) 0.5 (i.e., χο ) 0.5). In the

Eckelt et al.

Figure 10. Interrelation of the system specific parameters of eq 12 for aqueous solutions of pullulan and of dextran as compared with some solutions of synthetic polymers in organic solvents.5,8 With increasing temperature, the data points shift towards the left on the common line.

field of synthetic polymers, only the data for the relatively polar components poly(methyl methacrylate) and methyl acetate fall in the lower left quadrant.8 For the aqueous solutions of dextran and of pullulan the ζλ and R pairs are located well inside the lower left quadrant of such a plot. In these cases, favorable R < 0 values are combined with unfavorable ζλ < 0. Within the present temperature interval, the data shift along the common line to still lower R values as T rises, where this effect is much larger for pullulan than for dextran. When discussing the fundamental differences between typical solutions of synthetic polymers in organic solvents as compared with aqueous solutions of biopolymers it is worthy to note that the data for the system water/N-methyl morpholin N-oxide, a low molecular weight mixture to which we have also applied the present approach, also fall into the lower left quadrant21 of Figure 10. In this case, the absolute values of R and ζλ are, however, by 1 order of magnitude larger. The common denominator of the two types of systems lies in the prominent role hydrogen bonds play in the mixtures.

7. Conclusions The present study has revealed a number of fundamental differences between the thermodynamics of aqueous solutions of polysaccharides as compared with that of typical synthetic polymers in organic solvent. Two of these features can already be seen in the primary data, namely, in the composition dependence of vapor pressures. With synthetic polymers and organic solvents, the deviations of p above the solutions from po that of the pure solvent can hardly be noticed before the volume fraction of the polymer exceeds approximately 0.3–0.4. For the aqueous solution of pullulan on the other hand the corresponding concentration is roughly only half as large. The other particularity consists in the shape of the curves p(φ), which are sigmoidal for both polysaccharides, in contrast to the normal behavior; this finding means that the polymers interact uncommonly favorable with water as φ approaches unity such that it does not release the solvent into the vapor phase in the usual manner. A more detailed analysis of these observations in terms of the Flory–Huggins interaction parameters and their composition dependences discloses that χ(φ) may exhibit two extrema for the polysaccharides. For synthetic polymers, such a behavior has so far never been reported; one does sometimes encounter systems for which this curves passes either a minimum or a maximum, but never the two extrema conjointly. This particular feature of the aqueous solutions of polysaccharides is the reason why a hitherto very successful approach, which can for ordinary


polymer solutions model the entire diversity of composition dependencies quantitatively, fails for the present systems. To eliminate this deficiency, we have introduced an extra term in the expression for the integral interaction parameter g, which accounts for the necessity to distinguish between two types of water molecules: “normal” ones, clustering with other neighboring water molecules and “isolated” water molecules that bridge two segments of the polysaccharide. This generalization suffices to model all findings quantitatively by a total of three adjustable parameters. According to the above considerations, it is obvious that the particularities of the polysaccharide solution must vanish as φ and consequently the probability of the existence of “isolated” water approach zero; this feature opens a way to compare these aqueous solutions with the solutions of synthetic polymers in organic solvents in terms of the two parameters that need to be considered in both cases. These are R, the effect associated with the formation of a new contact between a solvent molecule and a polymer segment at fixed conformation (in the evaluation we have substituted R by χο) and ζλ, the effect resulting from the conformational relaxation into the equilibrium state. The outcome of this comparison is probably one of the most informative items of the present study because it reveals fundamental dissimilarities: For the solutions of synthetic polymers in organic solvents homogeneous mixing results in almost all cases from very favorable ζλ values in combination with unfavorable R values. For the present systems the situation is exactly the opposite: Highly favorable R values are associated with adverse ζλ values such that the Gibbs energy of each individual composition of the mixture assumes the minimum possible value. This observation immediately poses the question whether these features are of a more general nature and typical for aqueous systems. Presently, we can only answer it in part: The system water/cellulose (exhibiting a large miscibility gap) does not show the particularities of the present polysaccharide solutions. The R and ζλ values fall in the upper right quadrant6 of Figure 10 and ω j ) 0. To the knowledge of the authors the required detailed information on aqueous solutions of synthetic polymers is unfortunately not yet available. The present experiments have also documented some of the thermodynamic consequences of differences in the particular


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manner the individual glucose units are bound to each other in pullulan and in dextran. A comparison of the results for the lower molecular weight dextran (which should be unbranched) with that of the strictly linear pullulan has demonstrated that the latter polymer interacts considerably more favorable with water than the former. However, a more detailed assignment of the role the different kind of structures present in the two types of polysaccharide would require a much broader study, including measurements with low molecular weight model compounds.

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BM800217Y

Pullulan and Dextran: Uncommon Composition Dependent Flory

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